Notice that he takes a pause after telling each digit? That means he must be using single digit coded system (not XX or XXX), meaning he has 25000 images for Pi digits!. Suppose he uses method of loci to place the images, let's say he stores 3 images per locus (0-9 PAO), we get 25000/3 = 8333 loci to memorize. Now, he has to somehow enumerate the loci, let's say he assigns number to every 30th locus. That makes 25000/30 = 833 loci, and 734*3 + 90*2 + 9*1 = 2391 extra images to memorize. All in all we get 25000+8333+2391 ~= 36000 details to remember.

The time it would take?
If he memorizes on average 1 image in 8 seconds we get 8*36000 =288 000 s = 80h.
Let's say he reviews it 9 times before going to the show. Now he recalls an image in 4 seconds. We get 4*9*36000 = 1 296 000 s = 360h.
Together it makes 360 + 80 = 460h ~= 19 days. If he memorized 8h per day it would take him 57 days.

But a guy who can compose a triple sudoku in his mind surely has a faster system (not single digit) that I can't think of to memorize the digits of Pi.

Hey Paco keep going buddy. I personally know another mental calculator and fellow competitor, Mr. Jan Van Koningsveld from Germany (and Netherlands), who is an official judge of the http://www.pi-world-ranking-list.com website. During the Mental Calculation World Cup in 2012 (Giessen Mathematikum) and in 2014 (Dresden), I witnessed some π - Pi record trials and attempts by other people (during the breaks when one can try for new records). But I did not try myself, because I was focused on the competition, so reciting Pi to some digits would be an extra interference and distraction. But I may make some attempt in the future. For me even 2000 or 5000 would be an fantastic achievement, let alone 10 or 20 thousand. But if Rajveer Meena's actual new WR of 70 thousand is correct and verified, then that is incredible feat indeed.
A day has 86400 seconds, so for a recital rate of 1 digit per second, probably he needs almost 20 hours just to recite it. The problem is that even if I ever knew a 100 thousand digits, I could never break the world record, because after being awake 20+ hours I'd feel very drowsy and probably make a mistake somewhere. I find it extremely superhuman to be focused on something for 20+ hours consecutively, without getting dizzy or distracted.

I also read that a Japanese has done 86+ thousand π digits, but it was not confirmed. I am not sure if he made mistakes in the recital or if there were not official judges, but the fact he even attempted 86 thousand digits, that means he had memorised all those, which is an fantastic achievement itself, despite not making an official record. Another unbelievable thing is that we human beings, can not even flawlessly memorise a bunch of 100 thousand digits correctly, whereas for digital disks that's only a file of size just 100 Kilobytes, not even a millionth of an external hard drive. Despite all mnemnonics and calculation efforts it seems that we humans as a species are very inefficient when it come to brute-force of number encoding and their respective images association and representation in hippocampus and neocortex brain areas. But at least, we have to keep active what we got and keep practicing memorization.

We know that we humans, are now much worse than computers in mind sports, but we still do memorization in order to keep the brain active.
A related 'machine vs. human' analogy: the ISS (Space Station) speed is around 8 km/s, a thousand times faster than the human running speed at 8 m/s (e.g. which corresponds to the WR of 800 meters of Track&Field/Athletics , around 100 seconds for 800 m). Nevertheless, even if we humans made rockets and supersonic airplanes, we still run for hobbie or champion sports to keep active. The same applies for mind or memory sports (pi included) or chess.
I think the main gain for us, from such a routine activity (like Pi memorization), is the transferable skill of potentially memorising any information one wants (up the human limits though), and then store it in long-term memory.

Also, unlike the WMC Memory category of 1-hour decimals, which are presented and get forgotten afterwards (e.g. by the next day),
the π-Pi is a specific number however, and goes further into long-term memory, much more than '1-hour decimal numbers', which has a human WR of 2660, by W.Feng ( '11) http://www.world-memory-statistics.com/discipline.php?id=num60 , still amazing, but less in size than most Pi records.